Answer the following problems.
1. Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a hydraulic system. The piston chambers and the connecting tube are filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A1 and A2, respectively. A force F1 is exerted on piston 1. Rank the resultant force F2 on piston 2 that results from the combinations of F1, A1, and A2 given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking. (Use only “>” or “=” symbols. Do not include any parentheses around the letters or symbols.)
2. A bicycle tire pump has a piston with area 0.49 in2. If a person exerts a force of 24 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump?
3. A large truck tire is inflated to a gauge pressure of 82 psi. The total area of one sidewall of the tire is 1,330 in2. What is the net outward force (in lb) on the sidewall because of the air pressure? (Enter the magnitude.)
4. A viewing window on the side of a large tank at a public aquarium measures 59 in. by 69 in. The average gauge pressure from the water is 7 psi. What is the total outward force on the window?
5. The total mass of the hydrogen gas in the Hindenburg zeppelin was 18,000 kg. What volume did the hydrogen occupy? (Assume that the temperature of the hydrogen was 0°C and that it was at a pressure of 1 atm.)
6. A large balloon used to sample the upper atmosphere is filled with 590 m3 of hydrogen. What is the mass of the hydrogen (in kg)?
7. Find the gauge pressure (in psi) at the bottom of a freshwater swimming pool that is 18.6 ft deep.
8. The depth of the Pacific Ocean in the Mariana Trench is 36,198 ft. What is the gauge pressure at this depth?
9. An ebony log with volume 15.0 ft3 is submerged in water. What is the buoyant force on it (in lb)? (Enter the magnitude.)
10. An empty storage tank has a volume of 9,490 ft3. What is the buoyant force exerted on it by the air? (Assume the air is at 0°C and 1 atm.)
11. A modern-day zeppelin holds 9,770 m3 of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.)
12. A boat (with a flat bottom) and its cargo weigh 6,400 N. The area of the boat’s bottom is 5 m2. How far below the surface of the water is the boat’s bottom when it is floating in water?
13. A scale reads 378 N when a piece of iron is hanging from it. What does it read (in N) when it is lowered so that the iron is submerged in water?
14. A dentist’s chair with a person in it weighs 2000 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant’s foot exerts a force of 44 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston?
15. The wing of an airplane has an average cross-sectional area of 13 m2 and experiences a lift force of 91,000 N. What is the average difference in the air pressure between the top and bottom of the wing?
16. Air flows through a heating duct with a square cross-section with 9-inch sides at a speed of 4.1 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 15 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid.
17. A metal bowl with a weight of 1.45 N is placed in a larger kitchen container filled with olive oil. How much olive oil must the bowl displace in order to float? For reference, the mass density of olive oil is about 910 g/liter and its weight density is about 8.92 N/liter. Please give your answer in liters.
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